How do i solve this sequence
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How do i solve this sequence

[From: ] [author: ] [Date: 11-05-26] [Hit: ]
x, y,-8, 2, 12with d = 10and -8, 8,......
the first 3 terms of the sequence -8,x,y,72... form an arithmetic sequence while the 2nd 3rd and fourth terms form a geometric sequence. determine x and y

note: arithemtic : common difference
geometric: common ratio

thanks, this is suppperrrrr important:)

-
-8, x, y form arithmetic series

=> x + 8 = y - x

=> 2x = y - 8

x = (y/2) - 4 --------(1)

x, y, 72 are in geometric series

=> y/x = 72/y

=> y^2 = 72x

substitute x value from (1)

=> y^2 = 72 (y/2 - 4)

=> y^2 = 36y - 288

=> y^2 - 36y + 288 = 0

=> (y - 24)(y - 12) = 0

y = 12 and 24

x = (y/2) - 4

x = 2 and 8

The arithmetic sequences are

-8, 2, 12 with d = 10 and -8, 8, 24 with d = 16

The geometric sequences are

2, 12, 72 with r = 6 and 8, 24, 72 with r = 3
1
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